Cruz has faced criticism recently after GOP presidential front-runner Donald Trump began publicly questioning whether Cruz is eligible to president, even though he was born in Canada. Constitutional scholars have said it wasn't a problem, and Cruz denounced Canadian citizenship last year.

Trump has also repeated his belief that Cruz has a Canadian passport, which Cruz denied during a separate interview Wednesday with CNN's Dana Bash.

Romney's tweet references the conspiracy theory that arose during President Barack Obama's presidential campaign, when skeptics questioned whether the President was actually born in Hawaii, where he grew up, or Kenya, where his father is from.